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Additive functions for quivers with relations

Helmut Lenzing, Idun Reiten (1999)

Colloquium Mathematicae

Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when...

Additive functions on trees

Piroska Lakatos (2001)

Colloquium Mathematicae

The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing...

Additive radicals

Konstantin Igorevich Beidar, Katarina Trokanová-Salavová (1989)

Czechoslovak Mathematical Journal

Adjoint regular rings.

Heatherly, Henry E., Tucci, Ralph P. (2002)

International Journal of Mathematics and Mathematical Sciences

AE-rings

Manfred Dugas, Shalom Feigelstock (2004)

Rendiconti del Seminario Matematico della Università di Padova

AGQP-injective modules.

Zhu, Zhanmin, Zhang, Xiaoxiang (2008)

International Journal of Mathematics and Mathematical Sciences

Algebraic analysis in structures with the Kaplansky-Jacobson property

D. Przeworska-Rolewicz (2005)

Studia Mathematica

In 1950 N. Jacobson proved that if u is an element of a ring with unit such that u has more than one right inverse, then it has infinitely many right inverses. He also mentioned that I. Kaplansky proved this in another way. Recently, K. P. Shum and Y. Q. Gao gave a new (non-constructive) proof of the Kaplansky-Jacobson theorem for monoids admitting a ring structure. We generalize that theorem to monoids without any ring structure and we show the consequences of the generalized Kaplansky-Jacobson...

Algebraic characteristic classes for idempotent matrices.

Francisco Gómez (1992)

Publicacions Matemàtiques

This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.

Currently displaying 261 – 280 of 3997